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Task/Modular-inverse/Jq/modular-inverse.jq

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+# Integer division:
+# If $j is 0, then an error condition is raised;
+# otherwise, assuming infinite-precision integer arithmetic,
+# if the input and $j are integers, then the result will be an integer.
+def idivide($j):
+  . as $i
+  | ($i % $j) as $mod
+  | ($i - $mod) / $j ;
+
+# the multiplicative inverse of . modulo $n
+def modInv($n):
+  if $n == 1 then 1
+  else . as $this
+  | { r   : $n,
+      t   : 0,
+      newR: length, # abs
+      newT: 1}
+  | until(.newR == 0;
+        .newR as $newR
+        | (.r | idivide($newR)) as $q
+        | {r   : $newR,
+           t   : .newT,
+           newT: (.t - $q * .newT),
+           newR: (.r - $q * $newR) } )
+	
+  | if (.r|length) != 1 then "\($this) and \($n) are not co-prime." | error
+    else .t
+    | if .     < 0 then . + $n
+      elif $this < 0 then - .
+      else .
+      end
+    end
+  end ;
+
+# Example:
+42 | modInv(2017)